Thread: Limits question

Determine the limit:

lim x→−3 √ (x^2 + 7 − 4)/(x^2 − 9)

So I'm pretty sure it doesn't exist but i just wanted to make sure... i got it down to

√(x^2+3)/(x+3)(x-3)

which doesn't exist because it equals zero

thanks for any help

Originally Posted by smplease

Determine the limit:

lim x→−3 √ (x^2 + 7 − 4)/(x^2 − 9)

So I'm pretty sure it doesn't exist but i just wanted to make sure... i got it down to

√(x^2+3)/(x+3)(x-3)

which doesn't exist because it equals zero

thanks for any help

Multiplying by

You will get the answer to be either infinity or undefined..whichever your instructor prefers

This is because

Originally Posted by smplease

Determine the limit:

lim x→−3 √ (x^2 + 7 − 4)/(x^2 − 9)

So I'm pretty sure it doesn't exist but i just wanted to make sure... i got it down to

√(x^2+3)/(x+3)(x-3)

which doesn't exist because it equals zero

thanks for any help

For convenience, let f(x) = √(x^2+3)/(x+3)(x-3).

Note that but .

The left hand limit does not equal the right hand limit.

Therefore does not exist.